A Study of Effective Methods to Promote Foreign Trade Base on

Mathematical Analysis: A Case Study of Small and Medium-sized

Enterprises in China

Yin Ping

College of Financial Accounting, Zhejiang Institute of Economics and Trade, Hangzhou, Zhejiang, China

Keywords: Speeding Up the Export Tax Refund, The Gap between Export Trade Levy and Return, Mathematical

Analysis.

Abstract: In the post-epidemic era, how to effectively use the export tax rebate policy, expand the foreign trade of small

and medium-sized enterprises, and accelerate the formation of a new pattern of mutual promotion in both

domestic and international circles is one of the problems that the Chinese government urgently needs to solve.

From the mathematical analysis of nine cases before and after narrowing the gap between export trade levy

and return, it can be found that the effect of tax refund depends on the speed of tax refund. With the continuous

empowerment of digital technology and the promotion of tax service facilitation measures such as "Paperless",

"Non-contact" and "Processing of tolerance and shortage", the average processing cycle of export tax rebate

has been continuously compressed, on the premise of not increasing the financial pressure of governments at

all levels, the financial support to small and medium-sized production enterprises has been realized.

Production enterprises can set export tax rebate risk point through digital technology to avoid the loss of

export tax rebate benefits.

1 INTRODUCTION

In the post-epidemic era, how to effectively use the

export tax rebate policy, expand the foreign trade of

small and medium-sized enterprises, and accelerate

the formation of a new pattern of mutual promotion

in both domestic and international circles is one of the

problems that the Chinese government urgently needs

to solve. The export tax return is one of commonly

means of state intervention in the economy. It reduces

the cost of products, avoids repeat taxation, enhances

the competitiveness of goods in the international

market, and achieves the purpose of promoting

international trade through returning of part of the tax

on goods. In recent years, the state has continuously

increased the strength of export tax return, improved

the export tax return policy, and narrowing the gap

between export trade levy and return in China. But on

the other hand, the implementation of the policy has

also brought huge financial pressure to the central and

local governments.

1.1 Universality

Domestic scholars mostly analyze the impact of

export rebate on export trade in a single province or a

single commodity. (Luo, 2021) Some scholars

analyze the specific quantitative relationship between

export tax rebate and export trade of mechanical and

electrical products in Shanxi Province, and give some

policy suggestions. (Liu 2021,

Ren, 2021) Other

scholars combed through China’s agricultural export

tax rebate policy changes, analysis of the current

problems, put forward policy recommendations.

(Xie, 2021) Based on the above analysis, this paper

hopes to find out the foreign trade promotion policy

which is suitable for all small and medium-sized

enterprises and all commodities in China.

1.2 Sustainability

In the post-epidemic era, various countries

experienced different degrees of economic downturn

and the financial pressure of governments at all levels

increased. (Dai, 2018) To support the development of

China’s foreign trade in the post-epidemic era, some

532

Ping, Y.

A Study of Effective Methods to Promote Foreign Trade Base on Mathematical Analysis: A Case Study of Small and Medium-sized Enterprises in China.

DOI: 10.5220/0011189700003440

In Proceedings of the International Conference on Big Data Economy and Digital Management (BDEDM 2022), pages 532-536

ISBN: 978-989-758-593-7

scholars also mentioned that the tax policy of

lowering the tax base standard should not be used for

a long time. (Wang, 2021, Wang, 2021) Based on the

above analysis, this paper hopes to find out the

feasible policy that can effectively promote the

foreign trade of all small and medium-sized

enterprises without increasing the existing financial

pressure of governments at all levels.

2 MATERIALS AND METHODS

The export tax rebate policy of production enterprises

is different from that of foreign trade enterprises in

China. The export tax rebate for foreign trade

enterprises is the product of the purchase amount and

the export tax rebate rate. The export tax rebate policy

of production enterprises is more complicated. This

paper tries to find out the key factors that influence

the effect of policy through mathematical analysis of

the economic impact of narrowing the gap between

export trade levy and return of the production

enterprises.

2.1 Production Enterprises under the

General Trade Mode of "

CDR"(Cancel Deduct Return)

Policy

Under the general trade mode of production

enterprises, the "CDR" policy includes: "Cancel"

refers to the exemption from VAT on export sales,

"Deducted" refers to the amount of return payable

against the amount of tax payable, and "Return"

refers to the return of the part not covered by the

amount of deducted.

Under this policy, the accounting method of the

tax return for the production enterprise is as follows:

Suppose that the export sales in the current month

is α1, the sale tax is α2, the purchase tax is α3, the

leave tax for the previous period is α4, the sale tax

rate is ω1, the export tax return rate is ω2, the tax

cannot be cancelled and deducted for the current

period is α5, the tax payable for the current period is

α6, the "CDR" tax for the current period is α7, and the

tax return for the current period is α8. The "CD" tax

for the current period is α9, and the leave tax for the

next period is α10.

α5=α1×（ω1-ω2）

(1)

α6=α2-（α3-α5 ）-α4

(2)

α7=α1×ω2 (3)

According to the accounting results, the tax return

of production enterprises can be divided into three

situations:

If α6≥0；α8=0，α9=α7

(4)

If α6<0，and -α6≤α7；α8=-α6，

α9=α7-（-α6）

(5)

If α6<0 ， and -α6>α7 ； α8=α7 ，

α9=0，α10=-α6-α7

(6)

2.2 The Economic Impact of

Narrowing the Gap between

Export Trade Levy and Return on

Production Enterprises

In order to explain the economic impact of narrowing

the gap between export trade levy and return on the

production enterprises, it is assumed that the new tax

return rate is ω3, and ω3>ω2, the tax cannot be

cancelled and deducted for the current period is α5

the tax payable for the current period is α6

, the

"CDR" tax for the current period is α7

, and the tax

return for the current period is α8

. The "CD" tax for

the current period is α9

, and the leave tax for the next

period is α10

, and the rest is assumed as above. The

following are the accounting results of Production

enterprises under the new tax rate:

α5

=α1×（ω1-ω3）

(7)

α6

=α2-（α3-α5

）-α4

(8)

α7

=α1×ω3 (9)

If α6

≥0；α8

=0，α9

=α7

(10)

If α6

<0 ， and-α6

≤ α7

；α8

α6

，α9

=α7

-（-α6

）

(11)

If α6

<0，and-α6

>α7

；α8

=α7

，α9

=0，α10

=-α6

-α7

(12)

After the change of tax return rate, Production

enterprises may face nine situations. The following

analyzes the economic impact of narrowing the gap

between export trade levy and return on Production

enterprises one by one.

Before and after the change of tax return rate, the

conditions under which the enterprise all faces the

first kind are:

If α6≥0，and α6

≥0

Namely:

α2-（α3-α5 ）-α4≥0，and α2-（α3-α5

）-α4

≥0

After sorting out, we get:

α3+α4-α2≤α1×（ω1-ω3）

(13)

The economic impact of this situation is mainly

reflected in the reduction of the tax payable in the

current period:

A Study of Effective Methods to Promote Foreign Trade Base on Mathematical Analysis: A Case Study of Small and Medium-sized

Enterprises in China

533

α6-α6

=α2-（α3-α5 ）-α4-[α2-（

α3-α5

）-α4]

(14)

After sorting out, we get:

α1×（ω3-ω2 ）

(15)

Before and after the change of tax return rate, the

conditions under which the enterprise faces the

change from the first kind to the second kind are:

If α6≥0，and α6

<0，-α6

≤α7

Namely:

α2-（α3-α5 ）-α4≥0，α2-（α3-α5

）-α4<0 and

- [α2-（α3-α5

）-α4 ]≤α7

After sorting out, we get:

α1× (ω1-ω3) < α3+α4-α2≤α1×（

ω1-ω2）

(16)

The economic impact of this situation is mainly

reflected in the reduction of the tax payable in the

current period and the increase of the tax return:

α6+α8

=α2-（α3-α5 ）-α4-[α2-（

α3-α5

）-α4 ]

(17)

After sorting out, we get:

α1×（ω3-ω2 ）

(18)

Before and after the change of tax return rate, the

conditions under which the enterprise faces the

change from the first kind to the third kind are:

If α6≥0，and α6

<0，and -α6

>α7

Namely:

α2-（α3-α5 ）-α4≥0，α2-（α3-α5

）-α4<0, and

- [α2-（α3-α5

）-α4]> α7

After sorting out, we get:

α1×ω1<α3+α4-α2≤α1×（ω1-ω2

）

(19)

Because: α1×ω1>α1×（ω1-ω2 ）, the above

conditions cannot be met, so it is not possible.

Before and after the change of tax return rate, the

conditions under which the enterprise faces the

change from the second kind to the first kind are:

If α6<0，and -α6≤α7；α6

≥0

Namely:

α2-（α3-α5 ）-α4<0，-α2+（α3-α5 ）+α4≤α7

；α2-（α3-α5

）-α4≥0

After sorting out, we get:

α3+α4-α2≥α1×（ω1-ω2 ），and

α3+α4-α2≤α1×（ω1-ω3 ）

(20)

Because: α1×（ω1-ω2 ）>α1×（ω1-ω3 ）, the

above conditions cannot be met, so it is not possible.

Before and after the change of tax return rate, the

conditions under which the enterprise all faces the

second kind are:

If α6<0，and -α6≤α7；α6

<0，and -α6

≤α7

Namely:

α2-（α3-α5 ）-α4<0，-[α2-（α3-α5 ）-α4] ≤

α7；α2-（α3-α5

）-α4<0 and - [α2-（α3-α5

）-α4]

≤α7

After sorting out, we get:

α1×（ω1-ω2）<α3+α4-α2≤α1×ω1

(21)

The economic impact of this situation is mainly

reflected in the change of the tax return in the current

period:

α8

-α8=-[α2-（α3-α5

）-α4] + [α2-

（α3-α5 ）-α4]

(22)

After sorting out, we get:

α1×（ω3-ω2 ）

(23)

Before and after the change of tax return rate, the

conditions under which the enterprise faces the

change from the second kind to the third kind are:

If α6<0，and -α6≤α7；α6

<0，and -α6

>α7

Namely:

α2-（α3-α5 ）-α4<0，-[α2-（α3-α5 ）-α4] ≤

α7；α2-（α3-α5

）-α4<0 and - [α2-（α3-α5

）-α4]>

α7

After sorting out, we get:

α1×ω1<α3+α4-α2≤α1×ω1

(24)

The above conditions cannot be met, so it is not

possible.

Before and after the change of tax return rate, the

conditions under which the enterprise faces the

change from the third kind to the first kind are:

If α6<0，and -α6>α7；α6

≥0

Namely:

α2-（α3-α5 ）-α4<0，-[α2-（α3-α5 ）-α4]> α7

；α2-（α3-α5

）-α4≥0

After sorting out, we get:

α1×ω1<α3+α4-α2≤α1×（ ω1-ω3）

(25)

Because: α1×（ω1-ω3 ）<α1 ×ω1, the above

conditions cannot be met, so it is not possible.

Before and after the change of tax return rate, the

conditions under which the enterprise faces the

change from the third kind to the second kind are:

If α6<0，and -α6>α7；α6

<0，and -α6

≤α7

Namely:

α2-（α3-α5 ）-α4<0，and - [α2-（α3-α5 ）-α4]>

α7；α2-（α3-α5

）-α4<0 and - [α2-（α3-α5

）-α4]

≤α7

After sorting out, we get:

α1×ω1<α3+α4-α2≤α1×ω1

(26)

The above conditions cannot be met, so it is not

possible.

Before and after the change of tax return rate, the

conditions under which the enterprise all faces the

third kind are:

BDEDM 2022 - The International Conference on Big Data Economy and Digital Management

534

If α6<0，and -α6>α7；α6

<0，and -α6

>α7

Namely:

α2-（α3-α5 ）-α4<0，and - [α2-（α3-α5 ）-α4]>

α7；α2-（α3-α5

）-α4<0，and - [α2-（α3-α5

）

-α4]> α7

After sorting out, we get:

α3+α4-α2>α1×ω1 (27)

The economic impact of this situation is mainly

reflected in the increase of the tax return in the current

period:

α8

-α8 (28)

After sorting out, we get:

α1×（ω3-ω2 ）

(29)

3 RESULTS & DISCUSSION

3.1 The Greater the Export Sales, the

Stronger the Export Tax Rebate,

the Greater the Financial Pressure

Summarizing the above analysis, the economic

impact of narrowing the gap between export trade

levy and return on the production enterprises as

follows:

If α3+α4-α2≤α1×（ω1-ω3 ），

The reduction of the tax payable in the current

period:

α1×（ω3-ω2 ）

(29)

If α1×（ω1-ω3 ）<α3+α4-α2≤α1×（ω1-ω2 ）

，

The reduction of the tax payable in the current

period and the increase of the tax return in the current

period:

α1×（ω3-ω2 ）

(30)

If α1×（ω1-ω2 ）<α3+α4-α2≤α1×ω1，

The increase of the tax return in the current

period:

α1×（ω3-ω2 ）

(31)

If α3+α4-α2>α1×ω1，

The increase of the tax return in the current

period:

α1×（ω3-ω2 ）

(32)

For all enterprise, the reduction of the current tax

payable is:

α1×（ω3-ω2 ）

(33)

It can be seen that if α1 is increased, the reduction

of tax payable will be increased. On the other hand, if

ω3-ω2 is increased, the reduction of tax payable will

also be increased. In the meantime, the financial

pressure on governments at all levels will also

increase.

3.2 The Government Uses Digital

Technology to Expand the Effect of

Export Tax Rebate Policy

Although in each case, the economic impact of the

reduction of return difference on production

enterprises is consistent in amount, the impact on

capital flow is different. In the first case, the

enterprise can reduce capital outflow; in the second

case, it is reflected in the decrease of capital outflow

and the increase of capital inflow; in the latter two

cases, it is reflected in the increase of capital inflow.

The longer the enterprise gets the export tax refund,

the greater the difference of the tax refunds effect

among different types of production enterprises. In

the past, because the export tax rebate involved more

government departments, and the need to submit

more information, the return of export tax rebate

production enterprises often longer time. With the

continuous empowerment of digital technology and

the promotion of tax service facilitation measures

such as "Paperless", "Non-contact" and "Processing

of tolerance and shortage", the average processing

cycle of export tax rebate has been continuously

compressed, on the premise of not increasing the

financial pressure of governments at all levels, the

financial support to small and medium-sized

production enterprises has been realized.

3.3 Production Enterprises Use Digital

Technology to Avoid the Loss of

Export Tax Rebate Benefits

According to the above analysis, when α1 remains

constant, the economic benefits can be obtained as

follows:

If α3+α4-α2≤α1×（ω1-ω3 ），

The tax return in the current period is 0；

If α1×（ω1-ω3 ） <α3+α4+α2≤α1×ω1，

The tax return in the current period is

- [α2-（α3-α5

）-α4]

(34)

If α3+α4-α2>α1×ω1，

The tax return in the current period and the leave

tax for the next period are:

- [α2-（α3-α5

）-α4]

(35)

It can be seen that even if α1 is unchanged, when

the value of "α3+α4-α2" is in different ranges, the

economic benefits obtained by production enterprises

are also different. In the first case, the enterprise

A Study of Effective Methods to Promote Foreign Trade Base on Mathematical Analysis: A Case Study of Small and Medium-sized

Enterprises in China

535

cannot get all tax return, especially when α2-α3-

α4<α2×ω3, part of the tax return cannot be offset by

the sale tax, resulting in the reduction of economic

benefits for the enterprise. Therefore, production

enterprises can set export tax rebate risk point

through digital technology to avoid the loss of export

tax rebate benefits.

4 CONCLUSIONS

If the reduction of tax payable increases, production

enterprises can enjoy export tax rebate benefits, but

the financial pressure on governments at all levels

will also increase. In the post-epidemic era, we need

to adopt more effective, universal and sustainable

export tax rebate preferential policies to promote

foreign trade of small and medium-sized enterprises.

Through the above mathematical analysis, it can

be found: the government uses digital technology to

expand the effect of export tax rebate policy;

production enterprises can use digital technology to

avoid the loss of export tax rebate benefits.

The export tax rebate for foreign trade enterprises

is the product of the purchase amount and the export

tax rebate rate. The reduction of tax payable

increases, the financial pressure on governments at all

levels will also increase. The government uses digital

technology to expand the effect of export tax rebate

policy. However, foreign trade enterprises do not

exist the above-mentioned export tax rebate benefits

cannot enjoy the situation.

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Dai, Z.Q. (2018). An empirical analysis of the impact of

China’s import and export trade on tax revenue. J.

Science & Technology Ecnony Market. 08, 57–58.

Liu, X.H. & Ren S.Y. (2021). On the impact of export tax

rebate on China’s export trade. J. Productivity

Research. 5, 119-122.

Luo, G.H. (2021). Research on the influence of export tax

return on enterprise accounting and its

countermeasures. J. Enterprise Reform and

Management. 14, 111–113.

Wang, W.Q. & Wang, H. (2021). Considerations on China's

tax policy supporting the development of foreign trade

in post-epidemic era. J. Fiscal Science. 7, 84–94.

Xie, Y. (2021). The Influence of export tax rebate on China

s agricultural products trade and its countermeasures. J.

Shanxi Agricultural Economy. 4, 88–89.

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